A low-density parity-check (LDPC) code is a linear error correcting code. It may be used as a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph.
LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close (or even arbitrarily close on the binary erasure channel (BEC)) to the theoretical maximum (the Shannon limit) for a symmetric memory-less channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired.
Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length.